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Calculating Field by Method of Images due to Plane Wedged b/w Grounded Conductors

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Two semi-infinite grounded conductive planes meet at right angles. In the region b/w the conductors, there is the plane with angle 45° having surface charge density σ. Using the method of images, find the field distribution in this region.

    (There is a picture included, essentially showing the first quadrant, bounded by the two grounded planes, with the non-grounded plane at 45° above the x-axis).


    2. Relevant equations
    V=kq/r
    E*dA=σ*dA/ε


    3. The attempt at a solution

    First of all, I am making the assumption that determining the field means electric field and not potential. Most prior examples I have seen with method of images (MoI) usually works with getting potential, but maybe this is a different case?

    For MoI, there is a plane with +σ going up through 45°, so, mirroring how I would do this if this were a point charge, I put planes with -σ at 135° and -45° and then one with +σ at -135°. So basically two perpendicular, oppositely charged, infinite planes.

    I looked at this problem a very long time trying to calculate potential, but then I thought, can you just use Gauss's Law for each and confine your solution to the first quadrant? It seemed incredibly simple after that, but sometimes I make an incorrect assumption that oversimplifies the situation-- is this okay to assume?

    E=σ/2ε from the positive plane, and the direction is normal to the plane (-i/√2 +j/√2) and the direction from the negative plane is -i/√2 -j/√2 so that the after summing these components the field would be pointing in the -i direction. Is that the basic idea or have I made one too many assumptions?

    Thanks!
     
  2. jcsd
  3. Oct 12, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I think you have it. But, the final answer you gave has direction -i. Is that true everywhere in the first quadrant?
     
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